Q.In a permanent magnet at room temperature
Concept understanding — Magnetic Materials Magnetization
From a Paperclip to a Magnet: The Intuition
You already know that a magnet can pick up iron nails. But what is actually happening inside that nail when it gets near the magnet? And why does a plastic comb, rubbed on hair, pick up tiny bits of paper — but never iron filings?
The answer lies in magnetization — the process by which a material becomes magnetic.
Think of a piece of iron as a chaotic crowd of tiny compass needles. Each needle is an atomic magnetic moment (a tiny magnet, arising from the spin of electrons). In unmagnetized iron, these needles point in random directions. Their magnetic effects cancel out, so the iron as a whole shows no net magnetism.
Now bring a strong magnet close. Its magnetic field acts like a command: "Line up!" The tiny compass needles inside the iron start rotating, aligning themselves with the external field. The more they align, the stronger the iron's own magnetic field becomes. This alignment is magnetization.
Magnetization is not the same as inducing a current. It is a purely magnetic reorientation of atomic dipoles inside a material.
The Precise Definition
Magnetization (M) is the net magnetic dipole moment per unit volume of a material. It tells you how strongly a material is magnetized — how many tiny atomic magnets are aligned, and in which direction.
If a material has N atoms per unit volume, each with an average magnetic moment μavg, then:
M=Nμavg
The SI unit of M is amperes per metre (A/m). Why? Because a magnetic dipole moment has units of A·m², and dividing by volume (m³) gives A/m.
M=volumetotal magnetic dipole moment
How Magnetization Connects to the Magnetic Field
When a material gets magnetized, it produces its own magnetic field. The total magnetic field B inside the material is the sum of:
- The external applied field H (caused by free currents, like the current in a solenoid)
- The material's response — the magnetization M
The fundamental relation is:
B=μ0(H+M)
where μ0=4π×10−7T⋅m/A is the permeability of free space.
Do not confuse H (magnetic field intensity, or "magnetizing field") with B (magnetic flux density). H is what you apply; M is what the material does; B is the total field you measure.
The Three Kinds of Magnetic Materials
Not all materials respond the same way to an external field. The magnetization M is proportional to H for most materials (at least for small fields):
M=χmH
where χm is the magnetic susceptibility — a dimensionless number that tells you how easily a material magnetizes.
| Material Type | χm | Behaviour | Example |
|---|---|---|---|
| Diamagnetic | Small and negative (≈−10−5) | Weakly repelled by a magnet; M opposes H | Water, copper, bismuth |
| Paramagnetic | Small and positive (≈10−5 to 10−3) | Weakly attracted; M aligns with H | Aluminium, oxygen gas |
| Ferromagnetic | Large and positive (≫1) | Strongly attracted; M can be huge and persists even after H is removed | Iron, nickel, cobalt |
Ferromagnetic materials have spontaneous magnetization — their atomic moments align even without an external field, forming magnetic domains. Magnetization in these materials is not linear; it saturates and shows hysteresis.
A Simple Example
Take a long iron rod placed inside a solenoid carrying current I. The solenoid produces a uniform field H inside. The iron rod becomes magnetized: its atomic moments align, producing M in the same direction as H.
If χm for iron is about 5000, then M=5000H. The total field inside the rod becomes:
B=μ0(H+5000H)=μ0(5001)H
That is why an iron core can amplify the magnetic field of a solenoid by thousands of times.
The Bottom Line
Magnetization is the measure of how much a material becomes magnetic when placed in an external field. It arises from the alignment of atomic magnetic dipoles. For linear materials, M=χmH. For ferromagnets, the response is nonlinear, strong, and can be permanent — that is how you get a bar magnet from a piece of iron.
Magnetization and the classification of materials as diamagnetic, paramagnetic and ferromagnetic is a core topic of the NCERT Class 12 Physics chapter on magnetism and matter, tested regularly in CBSE boards and JEE Main. Students searching "diamagnetic paramagnetic ferromagnetic materials class 12 physics difference" will find this magnetic-susceptibility-based comparison matches the standard NCERT table.
Why this formula?
Magnetic Materials & Magnetization: Why the Key Formulas Hold
Let's build this from the ground up — starting with what magnetization physically means, then deriving the formulas step by step.
1. What is Magnetization (M)?
Magnetization is the net magnetic dipole moment per unit volume of a material.
- Inside a material, atoms act like tiny magnetic dipoles (due to electron spin and orbital motion).
- Without an external field, these dipoles point randomly → net M=0.
- When an external field H is applied, dipoles align partially → net M=0.
Definition:
M=volumenet magnetic dipole moment
Units: A/m (same as H).
2. The Fundamental Relation: B=μ0(H+M)
This is the master equation linking the three magnetic fields:
- B = magnetic flux density (the total field inside the material)
- H = applied magnetic field (due to free currents)
- M = magnetization (response of the material)
- μ0 = permeability of free space (4π×10−7 H/m)
Why this form?
Step 1: In vacuum, there is no material, so M=0. Then:
B=μ0H
Step 2: Inside a material, the dipoles themselves produce an additional field. The total B is the sum of:
- The field due to free currents (μ0H)
- The field due to bound currents (from aligned dipoles), which is μ0M
Hence:
B=μ0H+μ0M=μ0(H+M)
Key insight: M is not an independent field — it's the material's response to H.
3. Magnetic Susceptibility (χm) and Permeability (μ)
For linear, isotropic, homogeneous materials (most common in exams), magnetization is proportional to the applied field:
M=χmH
- χm = magnetic susceptibility (dimensionless)
- χm>0 for paramagnetic materials
- χm<0 for diamagnetic materials
- χm≫1 for ferromagnetic materials (but not linear!)
Derivation of relative permeability μr:
Substitute M=χmH into the master equation:
B=μ0(H+χmH)=μ0(1+χm)H
Define:
μr=1+χm(relative permeability)
μ=μ0μr(absolute permeability)
Thus:
B=μH
Why this matters: It shows that the material simply scales the applied field by a factor μr.
4. Why χm Has Different Signs (Physical Reasoning)
| Material Type | χm | Why? |
|---|---|---|
| Diamagnetic | χm<0 (small, ~10−5) | Applied field induces opposing dipole moments (Lenz's law at atomic level). M opposes H. |
| Paramagnetic | χm>0 (small, ~10−3) | Permanent atomic dipoles align partially with H. Thermal agitation fights alignment. |
| Ferromagnetic | χm≫1 (nonlinear) | Strong quantum-mechanical exchange coupling aligns dipoles spontaneously even without H. |
5. The Curie Law for Paramagnets (Temperature Dependence)
For paramagnetic materials, susceptibility depends on temperature:
χm=TC
where C is the Curie constant.
Why?
- Thermal energy (kBT) randomizes dipole alignment.
- Applied field H tries to align them.
- The competition leads to M∝TH.
From M=χmH, we get χm∝1/T.
Exam tip: Curie law holds for high temperatures and low fields. At very low T, saturation occurs.
6. Summary of Key Formulas (with "why")
| Formula | Why it holds |
|---|---|
| B=μ0(H+M) | Total field = free-current field + bound-current field |
| M=χmH | Linear response approximation (for small fields) |
| μr=1+χm | Direct substitution into B=μ0μrH |
| χm=C/T (Curie law) | Thermal agitation vs. field alignment |
Final takeaway: Magnetization is the material's voice — it tells you how the internal dipoles respond to an external magnetic nudge. The formulas are just a mathematical translation of that physical conversation.
A permanent magnet is a ferromagnet, so each molecule already carries a non-zero magnetic moment (a wrong). Its magnetism comes from domains — regions of aligned moments. In a real permanent magnet at room temperature the domains are only partially aligned (thermal agitation and pinning prevent perfect saturation), giving a strong but sub-saturation net moment. Neither the individual molecular moments nor the domains are perfectly aligned (b and d wrong).
Correct option: (c) domains are partially aligned.
A permanent magnet is a ferromagnetic material whose net magnetisation comes from magnetic domains. At room temperature these domains are only partially aligned, not perfectly. Correct option: (c).
Concept understanding. In a ferromagnet the atoms/molecules carry permanent magnetic moments that couple through the exchange interaction into domains — small regions in which the moments point the same way. In an unmagnetised sample the domains point in random directions and cancel. Magnetising the material makes the domains grow/rotate toward the field, leaving a net moment when the field is removed. Room temperature (≈300 K) is far below the Curie temperature of common magnets (iron Tc≈1043 K), so a large net magnetisation survives — but thermal agitation and domain-wall pinning keep it below saturation.
Testing each option.
- (a) In a ferromagnet each molecule has a non-zero magnetic moment; that is the very origin of the effect. Wrong.
- (b) The molecular moments are not all perfectly aligned — thermal energy tilts and randomises them, and only within a domain do they roughly agree. Wrong.
- (c) The correct picture: the material's magnetisation is produced by domains that are partially aligned, giving a strong but sub-saturation moment. Correct.
- (d) Domains being all perfectly aligned would mean full saturation, which does not hold at ordinary temperature for a real permanent magnet. Wrong.
Correct option: (c) domains are partially aligned. The molecular moments are non-zero (ruling out a) but neither the moments (b) nor the domains (d) are perfectly aligned at room temperature.
Method: Reasoning About Ferromagnetic Domain Alignment
Use this elimination approach for conceptual questions about the state of magnetisation inside a permanent magnet or ferromagnetic sample.
Steps
Step 1: Recall the two-level structure of a ferromagnet
Individual atoms/molecules each carry a nonzero magnetic moment — this is what makes the material ferromagnetic in the first place, and it is never zero. These moments group into domains: regions where neighbouring moments are aligned by the exchange interaction.
Step 2: Distinguish "molecular alignment" from "domain alignment"
A claim that individual molecular moments are all "perfectly aligned" is a much stronger — and generally false — statement than a claim about domains being aligned. Thermal agitation always tilts individual moments somewhat, even within an aligned domain, so treat any "perfectly aligned molecules" option with suspicion.
Step 3: Judge the degree of domain alignment against temperature
At ordinary (room) temperature, below the Curie temperature, domains are real but only partially aligned. Full/perfect alignment (saturation) would need either a very strong external field or a temperature near absolute zero; at room temperature, thermal effects and domain-wall pinning keep the material below saturation.
Step 4 (Applying to this problem): Eliminate the zero-moment and perfect-alignment extremes
Reject any option claiming molecular moments are zero (contradicts ferromagnetism itself) or that alignment is "perfect" (contradicts realistic room-temperature behaviour). The physically correct middle ground — partial domain alignment — is what a real permanent magnet at room temperature shows.
- CBSE 2026Set 55/1/11 markMCQQ.For questions 13 to 16, two statements are given – one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) below: (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Both Assertion (A) and Reason (R) are false. Assertion (A) : All atoms have a net magnetic moment. Reason (R) : A current loop does not always behave as a magnetic dipole.
›Reveal solutionSolution
The key idea is that not all atoms have a net magnetic moment — only those with unpaired electrons do. The reason given is also false because a current loop always behaves as a magnetic dipole. Therefore both statements are false.
Understanding the Concept
The magnetic moment of an atom arises primarily from two sources: the orbital motion of electrons (like tiny current loops) and the intrinsic spin of electrons. For an atom to have a net magnetic moment, these contributions must not cancel out completely.
In most atoms, electrons fill orbitals in pairs. Within each pair, the two electrons have opposite spins, so their spin magnetic moments cancel. Similarly, if all orbitals are completely filled, the orbital angular momentum also sums to zero. Only atoms with unpaired electrons — like iron, cobalt, nickel — possess a permanent net magnetic moment. Atoms like helium or neon, with all electrons paired, have zero net magnetic moment.
Now examine the two statements:
-
Assertion (A): "All atoms have a net magnetic moment." This is false — as explained, atoms with completely filled shells (noble gases, for example) have no net magnetic moment.
-
Reason (R): "A current loop does not always behave as a magnetic dipole." This is also false. Any current loop, regardless of shape or size, produces a magnetic field that at large distances is exactly that of a magnetic dipole. The magnetic dipole moment of a current loop is m=IA, where I is the current and A is the area vector. This is a fundamental result in electromagnetism.
Watch outA common mistake is to think that because some atoms are non-magnetic, a current loop might also sometimes fail to be a dipole. But the two ideas are unrelated — a current loop is always a magnetic dipole, while an atom is only magnetic if it has unpaired electrons.
TipThe magnetic dipole moment of a current loop is a definition — it's not a property that appears or disappears. Even a loop carrying zero current has zero dipole moment, but it still behaves as a dipole (just a zero-strength one). The statement "does not always behave as a magnetic dipole" is therefore meaningless in physics.
Step-by-Step Reasoning
-
Evaluate Assertion (A):
Atoms with completely filled electron shells (e.g., He, Ne, Ar) have all electrons paired. Their spin magnetic moments cancel, and their orbital angular momentum is zero. Hence they have zero net magnetic moment. The assertion claims all atoms have a net magnetic moment — this is clearly false.
-
Evaluate Reason (R):
A current loop, by definition, has a magnetic dipole moment m=IA. Its magnetic field at distances large compared to the loop's size is identical to that of a magnetic dipole. There is no condition under which a current loop ceases to behave as a magnetic dipole. The reason is therefore false.
-
Determine the relationship:
Since both statements are false, the correct code is (D): Both Assertion (A) and Reason (R) are false.
✓Final answerThe correct option is (D) — both Assertion (A) and Reason (R) are false.
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- CBSE 2026Set A1 markMCQQ.Relative permeability is equal to (A) μr = μ0·μ (B) μr = μ/μ0 (C) μr = μ0/μ (D) μr = √(μ·μ0)
›Reveal solutionSolution
Relative permeability μr = μ/μ₀ (a dimensionless ratio).
Relative permeability compares the magnetic permeability of a material with that of free space:
μr=μ0μ
It is a pure (dimensionless) number that tells how much more (or less) magnetisable a medium is than vacuum. For vacuum μr=1; for a ferromagnet it is very large.
✓Final answer(B) μr = μ/μ0.
- CBSE 2026Set ANNUAL1 markQ.Write the relation between magnetisation (M), magnetic intensity (H) and magnetic field (B) of a substance.
›Reveal solutionSolution
A material's total magnetic field B combines the externally applied field (through H) and the material's own induced magnetisation M.
When a magnetic material is placed in an external magnetising field, it develops a magnetisation M (net magnetic moment per unit volume) in response to the magnetic intensity H present. The resultant magnetic field B inside the material is the sum of the contribution due to H and the contribution due to the material's own magnetisation M, combined as:
B = mu0 (H + M)
where mu0 is the permeability of free space. This relation holds for all magnetic materials (dia-, para- and ferromagnetic).
✓Final answerB = mu0 (H + M).
- CBSE 2024Set ANNUAL1 markQ.The resultant magnetic moment produced per unit volume of a substance is called __________.
›Reveal solutionSolution
Magnetisation M is defined exactly as the net magnetic moment per unit volume of a material.
When a magnetic material is placed in an external field, the atomic dipole moments tend to align, producing a net magnetic moment in the sample. The magnetisation is defined as:
M=volumenet magnetic moment=Vmnet
It has the same units as the magnetic field intensity H (A/m), and quantifies how strongly a material has been magnetised by the applied field.
✓Final answerMagnetisation (M).
- CBSE 2022Set I1 markMCQQ.Intensity of a magnetising field (H) is equal to (A) B_0/μ_0 (B) μ_0/B_0 (C) B_0 μ_0 (D) √(B_0 μ_0)
›Reveal solutionSolution
The magnetic field and magnetising field are related by B = μ_0 H (in vacuum), so H = B_0/μ_0.
The magnetic intensity (magnetising field) H describes the field produced by free currents alone, independent of the medium. In free space (vacuum) the total field B_0 is related to H by B0=μ0H.
Rearranging gives H=B0/μ0, whose SI unit is ampere/metre (A/m).
Options (c) B_0μ_0 and (d) √(B_0μ_0) have wrong dimensions, and (b) inverts the relation.
✓Final answer(A) B_0/μ_0 — from B_0 = μ_0 H, the magnetising field is H = B_0/μ_0.
- CBSE 2022Set I1 markMCQQ.Relative permeability is equal to (A) μ/μ_0 = μ_r (B) μ_0/μ = μ_r (C) μ_r = μ·μ_0 (D) √(μ_0 μ) = μ_r
›Reveal solutionSolution
Relative permeability μ_r = μ/μ_0.
The relative permeability of a material is the ratio of its absolute permeability μ to the permeability of free space μ₀:
μr=μ0μ.
It is a dimensionless number (μ_r ≈ 1 for vacuum/air, ≫ 1 for ferromagnets).
✓Final answer(A) μ/μ_0 = μ_r.
- CBSE 2021Set A1 markMCQQ.Which of the following relations is correct for permeability? (A) μ = H/B (B) μ = B/H (C) μ = B.H (D) μ = (B + H)
›Reveal solutionSolution
Permeability μ = B/H.
Inside a magnetic material the magnetic flux density B is related to the magnetising field intensity H by B = μH, where μ is the (absolute) permeability of the material. Rearranging:
μ=HB
It describes how readily the medium allows magnetic field lines to pass through it. For free space μ = μ₀ = 4π × 10⁻⁷ T·m/A.
✓Final answer(B) μ = B/H.
- CBSE 2018Set ANNUAL1 markQ.The resultant magnetic moment of diamagnetic and paramagnetic substance are zero and finite respectively. Why?
›Reveal solutionSolution
Diamagnetic atoms have fully paired electrons (moments cancel → zero); paramagnetic atoms have unpaired electrons (moments don't cancel → finite).
Each electron in an atom has a magnetic moment due to its orbital motion and its spin. The net atomic moment is the vector sum of all these electron moments.
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Diamagnetic substances: every electron is paired with another of opposite spin/orbital moment, so the individual moments cancel completely. The resultant magnetic moment of the atom is therefore zero. (Such materials are only weakly repelled by a field, an effect induced by the applied field itself.)
-
Paramagnetic substances: they contain one or more unpaired electrons. These unpaired moments cannot fully cancel, so the atom is left with a finite (non-zero) permanent magnetic moment, and the material is weakly attracted into a magnetic field.
✓Final answerDiamagnetic atoms have all electron moments paired and cancelling (zero resultant), while paramagnetic atoms have unpaired electrons giving a finite resultant magnetic moment.
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